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Adding local short description: "Device used in physical therapy", overriding Wikidata description "trademark" |
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Inside the outer shell, the spinning mass is fixed to a thin metal [[axle]], each end trapped in a circular, equatorial groove in the outer shell. A lightweight ring with two notches for the axle ends rests in the groove. This ring can slip in the groove, allowing the ball to spin perpendicular to the rotational axis of the ring.
To increase the [[angular velocity]] of the ball, the sides of the groove exert forces on the ends of the axle. The normal and axial forces will have no effect, so the tangential force must be provided by the [[friction]] of the ring acting on the axle. The user can apply a [[torque]] on the ball by tilting the shell in any direction except in the plane of the groove or around an axis aligned with the axle. The tilting results in a shift of the axle ends along the groove. The direction and speed of the shift can be found from the formula for the [[precession]] of a [[gyroscope]]: the applied torque is equal to the [[cross product]] of the [[angular velocity]] of precession and the [[angular momentum]] of the spinning mass. The rate of rotation of the internal ball increases as the total amount of torque applied is increased. The direction of the torque does not matter, as long as it is perpendicular to the plane of rotation of the ball. The friction of the ring increases on the side opposite to the plane of rotation. This process obeys symmetry across the plane perpendicular to the axle. The only restriction to this process is that the relative speed of the surface of the axle and the side of the groove due to precession, <math>\mathit{\Omega}_{\mathrm{P}} R_{\mathrm{groove}}</math>, must exceed the relative speed due to the rotation of the spinning mass, <math>\omega r_{\mathrm{axle}}</math>. The minimum torque required to meet this condition is <math> I \omega^2 \left( r_{\mathrm{axle}} / R_{\mathrm{groove}} \right) </math>, where '''I''' is the [[moment of inertia]] of the spinning mass, and '''ω''' is its [[
Since [[angular acceleration]] will occur regardless of the direction of the applied torque, as long as it is large enough, the device will function without any fine-tuning of the driving motion. The tilting of the shell does not have to have a particular rhythm with the precession or even have the same frequency. Since [[Friction|kinetic friction]] is usually almost as strong as [[Friction|static friction]] for the materials typically used, it is not necessary to apply exactly the amount of torque needed for the axle to roll without slipping along the side of the groove. These factors allow beginners to learn to speed up the rotation after only a few minutes of practice.
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